Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2007; 44(5): 1065-1078

Printed September 1, 2007

Copyright © The Korean Mathematical Society.

Global solutions of semirelativistic Hartree type equations

Yonggeun Cho and Tohru Ozawa

Pohang University of Science and Technology, Hokkaido University

Abstract

We consider initial value problems for the semirelativistic Hartree type equations with cubic convolution nonlinearity $F(u) =(V * |u|^2)u$. Here $V$ is a sum of two Coulomb type potentials. Under a specified decay condition and a symmetric condition for the potential $V$ we show the global existence and scattering of solutions.

Keywords: semirelativistic Hartree type equations, global existence, scattering, Coulomb type potentials

MSC numbers: 35Q40, 35Q55, 47J35